## D

Figure 2.5 {Continued)

Mass Balance

Component Balance

Energy Balance

AH. + FJifjt + Vn+1Hv>tl + Ln.lHLji.i = VnHVjx + L^ (2.3) Equilibrium Relationship y* - Kxn (2.4)

In multicomponent distillation of j components, there are j - 1 component balances and j - 1 equations describing the equilibrium relationship.

Multiple stages (Fig. 2.5b). Equations (2.1) to (2.4) apply to each stage. A rigorous solution (Chap. 4) simultaneously solves these equations for each stage and each component. The equations can be simplified and solved by analytical shortcut procedures (Chap. 3) or graphically. The rest of this chapter focuses on the graphical procedures, which are applied to introduce and illustrate several key fractionation concepts.

### 2.2 x-y Diagrams

Computers have superseded graphical techniques as the main distillation design and performance evaluation tool. Nevertheless, graphical techniques are still widely used in modern distillation technology. Their prime application is as an analytical tool. They provide a means of visualizing the process and enable spotting pinched conditions, excessive reflux, incorrect feed points, and a nonoptimum thermal condition of the feed. They are powerful for analyzing computer solutions (Sec. 2.4.1). Other applications are screening and optimization of design options, providing initial estimates for computer calculations and engineer training.

The graphical technique most frequently used in distillation is the x-y or McCabe-Thiele diagram (1). The H-x, or Ponchon-Savarit diagram (2,3), is harder to visualize and cannot be readily extended to multicomponent distillation. Due to their limited application, H-x diagrams were excluded from this book, and are discussed elsewhere (4-6).

2.2.1 McCabe-Thiele diagrams: fundamentals

A mass balance for the "envelope" shown in Fig. 2.6a, cutting below any plate n in the rectifying section, gives

yn+i

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